6.4.2.3Half-lives and the random nature of radioactive decay
AQA GCSE Combined Science Foundation (8464), Foundation tier · Physics › Atomic structure › Atoms and nuclear radiation
Practise Half-lives and the random nature of radioactive decay. 6 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
What half-life means, how it links to the random nature of radioactive decay, and how to find a half-life from a graph or data. Expect graph reading and 2 to 4 mark calculations.
Key facts
Half-life: time for the number of unstable nuclei in a sample (or its count rate) to halve
Radioactive decay is random: you cannot predict which nucleus decays or when
Number of half-lives = time passed ÷ half-life
Fraction left after 0, 1, 2, 3, 4 half-lives: 1, 1/2, 1/4, 1/8, 1/16
Subtract the background count rate before finding a half-life
Notes
Random decay
Radioactive decay is random. You cannot predict which nucleus in a sample will decay next, or when a particular nucleus will decay.
But a sample contains a huge number of nuclei, so the fraction that decays in a given time is predictable. That is why each isotope has its own fixed half-life.
Half-life
The half-life of a radioactive isotope is the time it takes for the number of nuclei of the isotope in a sample to halve.
It is also the time it takes for the count rate (or activity) from a sample containing the isotope to fall to half its initial level.
After each half-life the activity halves again, e.g. 800 Bq → 400 Bq → 200 Bq → 100 Bq after 3 half-lives.
Number of half-lives = time passed ÷ half-life.
Finding the half-life from a graph
diagram
Choose a starting value on the curve that is easy to halve, e.g. 600 Bq, and read the time.
Find where the activity is half that value (300 Bq) and read that time.
The difference between the two times is the half-life. Repeat from another starting value and take the mean.
The activity halves every 2 hours (800 → 400 → 200 Bq), so the half-life is 2 hours.
If the readings include background radiation, subtract the background count rate first.
How to answer each type of question
Define half-life and random decay
1 to 2 marksGrade 5
Half-life: 'the time taken for the number of unstable nuclei (or the count rate) to halve'.
Random: 'cannot predict which nucleus will decay next, or when'.
Example. (a) Define the half-life of a radioactive isotope. (1 mark) (b) Radioactive decay is random. Explain what this means. (1 mark)
Show the model answerHide the model answer
(a) The time taken for the number of unstable nuclei of the isotope in a sample to halve (1) (b) You cannot predict which nucleus will decay next, or when a particular nucleus will decay (1)
Don’t lose marks
Thinking that after two half-lives the sample has all gone. A quarter is left.
Dividing the time by 2 instead of by the half-life to find the number of half-lives.
Forgetting to subtract the background count rate before finding the half-life.
Defining half-life as 'half the time it takes for the sample to decay completely'.
More tips
Memory tricks
Halving table: write time and activity in two columns, and halve down the columns until you reach the value you need.
Calculator: 0.5^n gives the fraction left, e.g. 0.5^4 = 0.0625 = 1/16.
Sense check: 1 half-life leaves a half, 2 leave a quarter, 3 leave an eighth.
On a graph, draw lines across to the curve and down to the time axis so the examiner can see your readings.
Exam technique
Show each halving step, e.g. 2400 → 1200 → 600 → 300, so your method is clear.
When reading a graph, pick a starting value that is easy to halve and read to the nearest small square.
What each grade needs
What you need to be able to do, from the first marks up to the top grade.
Grade 4
Define half-lifeThe time for the number of unstable nuclei in a sample, or its count rate, to halve.
Grade 5
Explain what random decay meansYou cannot predict which nucleus will decay or when, but a large sample decays in a predictable way.
Grade 5
Find a half-life from a graphRead the time for the activity or count rate to fall to half of any starting value.
Quick recall
Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.
A sample of a radioactive isotope has an activity of 800 Bq. The half-life of the isotope is 2 days. What is the activity of the sample after 2 days?
400 Bq
Sample questions
Written for this site in the style of AQA exam questions. They are not taken from real past papers.
Question 1Easy4 marks
(a) What is meant by the half-life of a radioactive isotope? Tick (✓) one box.[1]
The time it takes for the number of unstable nuclei in a sample to halve
Half of the time it takes for all the nuclei in a sample to decay
The time it takes for the mass number of a nucleus to halve
The time it takes for a nucleus to lose half of its protons
(b) A sample of a radioactive isotope has an activity of 800 Bq. The half-life of the isotope is 2 days. What is the activity of the sample after 2 days?[1]
(c) What is the activity of the sample after 6 days?[1]
(d) Radioactive decay is random. What does this mean?[1]
Show the answer and mark scheme
(a)Answer: The time it takes for the number of unstable nuclei in a sample to halve
(b)Answer: 400 Bq
400 (Bq)
(c)Answer: 100 Bq
100 (Bq)
(d)Answer: You cannot predict when a particular nucleus will decay.
it is not possible to predict which nucleus will decay next / when a particular nucleus will decay
Question 2Medium3 marks
After 3 half-lives, the activity of a radioactive sample is 15 Bq. Calculate its initial activity.[3]
Show the answer and mark scheme
Answer: 120 Bq
after 3 half-lives, activity = initial activity ÷ 8